From above analysis of the track events, we find that 12 of 15 track events can be associated with GRBs
if taking the large errors in both time and direction into consideration. What is more, even if we do not take these errors into
consideration but use the same error estimation with shower events, we can still find 3 track events that can be
associated with GRB candidates and satisfy the same regularity found in TeV and PeV shower events [1]}, [2]}.
Therefore our results of track events are consistent with the shower events to associate high energy cosmic neutrinos with GRBs with a same Lorentz violation scale \(E_{\mathrm {LV}}\) ,
which is the only free parameter that can be determined by a single event in principle. One can easily finger out that the
significance of our result is very high considering that 12 shower events and also 12 track events fall on
a same line with a fixed \(E_{\mathrm {LV}}\) .
It is interesting to notice that there are both time “delay” and “advance” events,
as can be seen from Table REF , thus the track events also support the proposal [2]} of Lorentz violation with different propagation properties between neutrinos and anti-neutrinos.
